We consider Cauchy completeness in the double categories of toposes, topological spaces, locales, and other suplattice based settings. We also present a uniform approach to the relationship between adjoints and projectivity in double categories with applications to (not-necessarily commutative) rings, rigs, and quantales.
Keywords: double categories, Cauchy completeness, sober spaces, quantales, projectives
2020 MSC: 18N10, 18F70, 18F75, 18D20, 18G05
Theory and Applications of Categories, Vol. 43, 2025, No. 1, pp 9-22.
Published 2025-02-25.
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